A remark on Nehari-type oscillation criteria for self-adjoint linear differential equations
Došlý, Ondřej ; Fiedler, Frank
Commentationes Mathematicae Universitatis Carolinae, Tome 32 (1991), p. 447-462 / Harvested from Czech Digital Mathematics Library

Oscillation criteria of Nehari-type for the equation $(-1)^n(x^{\alpha}y^{(n)})^{(n)} + q(x)y = 0$, $\alpha\in {\bold R}$, are established. These criteria impose no sign restriction on the function $q(x)$ and generalize some recent results of the second author.

Publié le : 1991-01-01
Classification:  34A30,  34C10
@article{118426,
     author = {Ond\v rej Do\v sl\'y and Frank Fiedler},
     title = {A remark on Nehari-type oscillation criteria for self-adjoint linear differential equations},
     journal = {Commentationes Mathematicae Universitatis Carolinae},
     volume = {32},
     year = {1991},
     pages = {447-462},
     zbl = {0751.34017},
     mrnumber = {1159793},
     language = {en},
     url = {http://dml.mathdoc.fr/item/118426}
}
Došlý, Ondřej; Fiedler, Frank. A remark on Nehari-type oscillation criteria for self-adjoint linear differential equations. Commentationes Mathematicae Universitatis Carolinae, Tome 32 (1991) pp. 447-462. http://gdmltest.u-ga.fr/item/118426/

Coppel W.A. Disconjugacy, Lectures Notes in Math. No. 220, Springer Verlag, Berlin-Heidelberg, 1971. | MR 0460785 | Zbl 0224.34003

Došlý O. The existence of conjugate points for self-adjoint linear differential equations, Proc. Roy. Soc. Edinburgh 112A, (1989), 73-85. | MR 1025455

Došlý O. Oscillation criteria for self-adjoint linear differential equations, submitted to Diff. Integral Equations.

Fiedler F. Hinreichende Oszillationkriterien für gewöhnliche Differentialoperatoren höher Ordnung, Math. Nachr. 96 (1980), 35-48. (1980) | MR 0600799

Fiedler F. Oszillationkriterien vom Nehari-Typ für gewöhnliche Differentialoperatoren vierter and sechster Ordnung, Beiträge Anal. 18 (1981), 113-132. (1981) | MR 0650144

Fiedler F. Oscillation criteria for a class of $2n$-order ordinary differential operators, J. Diff. Equations 42 (1981), 155-185. (1981) | MR 0641646 | Zbl 0452.34031

Fiedler F. Oscillation criteria for a special class of $2n$-order ordinary differential equations, Math. Nachr. 131 (1987), 205-218. (1987) | MR 0908812 | Zbl 0644.34024

Glazman I.M. Direct Methods of Qualitative Spectral Analysis of Singular Differential operators, Davey, Jerusalem, 1965. | MR 0190800 | Zbl 0143.36505

Lewis R.T. Oscillation and nonoscillation criteria for some self-adjoint even order linear differential operators, Pacific J. Math. 51 (1974), 221-234. (1974) | MR 0350112 | Zbl 0281.34027

Müller-Pfeiffer E. Oscillation criteria of Nehari-type for Schrödinger equation, Math. Nachr. 96 (1980), 185-194. (1980) | MR 0600809

Nehari Z. Oscillation criteria for second order linear differential equations, Trans. Amer. Math. Soc. 85 (1957), 428-445. (1957) | MR 0087816 | Zbl 0078.07602